Two types of minimax theorems for vector-valued functions
type: Item
instance of: scholarly article
title: Two types of minimax theorems for vector-valued functions
zbMATH Open document ID: 0696.90060
DOI: 10.1007/BF00941571
published in: Journal of Optimization Theory and Applications
publication date: 1991-01-01T00:00:00Z
review text: It seems that minimax theorems for vector-valued functions found in recent papers have something in common. Taking note of this, we improve several results in the author's recent works and state two types of minimax theorems for vector-valued functions. One theorem refers to functions with some special convexity properties; the other theorem refers to separated functions of the type \(f(x,y)=u(x)+v(y)\). The proofs are based on the existence of weak cone saddle points of f and on a condition about a pointed convex cone which induces a partial ordering in the image space of f. We need the condition \((C\setminus \{0\})+cl C\subset C\), which implies the Sterna-Karwat condition for a convex cone C of a Hausdorff topological vector space.
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 49K35
Mathematics Subject Classification ID: 46A99
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 4141809
zbMATH Keywords: C-convex functions
zbMATH Keywords: minimax theorems
zbMATH Keywords: vector-valued functions
zbMATH Keywords: weak cone saddle points
zbMATH Keywords: pointed convex cone
zbMATH Keywords: Sterna-Karwat condition
zbMATH Keywords: Hausdorff topological vector space
author: Tamaki Tanaka
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00941571
OpenAlex ID: W2068872980
description: scientific article; zbMATH DE number 4141809